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The abundance distribution in the ejecta of the peculiar slowly declining Type Ia supernova (SN\,Ia) SN\,1999aa is obtained by modelling a time series of optical spectra. Similar to SN\,1991T, SN\,1999aa was characterised by early-time spectra dominated by \FeIII\ features and a weak \SiII\,6355\,Å line, but it exhibited a high-velocity \CaII\,H\&K line and morphed into a spectroscopically normal SN\,Ia earlier. Three explosion models are investigated, yielding comparable fits. The innermost layers are dominated by $\sim 0.3$\,\Msun\ of neutron-rich stable Fe-group elements, mostly stable iron. Above that central region lies a \Nifs-dominated shell, extending to $v \approx 11,000$ -- $12,000$\,\kms, with mass $\sim 0.65$\,\Msun. These inner layers are therefore similar to those of normal SNe\,Ia. However, the outer layers exhibit composition peculiarities similar to those of SN\,1991T: the intermediate-mass elements shell is very thin, containing only $\sim 0.2$\,\Msun, and is sharply separated from an outer oxygen-dominated shell, which includes $\sim 0.22$\,\Msun. These results imply that burning suddenly stopped in SN\,1999aa. This is a feature SN\,1999aa shares with SN\,1991T, and explain the peculiarities of both SNe, which are quite similar in nature apart from the different luminosities. The spectroscopic path from normal to SN\,1991T-like SNe\,Ia cannot be explained solely by a temperature sequence. It also involves composition layering differences, suggesting variations in the progenitor density structure or in the explosion parameters.